# How do you solve 15- 2\sqrt { x + 3} = 7?

Aug 1, 2017

See below.

#### Explanation:

Rearranging the common parts together,

$15 - 2 \setminus \sqrt{x + 3} = 7$

$8 = 2 \setminus \sqrt{x + 3}$

$4 = \setminus \sqrt{x + 3}$

Squaring both sides,

$16 = x + 3$

$x = 13$

We must make sure this is not extraneous.

$\sqrt{13 + 3} = \sqrt{16 > 0}$, so this solution is real. Thus, our only real solution is $x = 13$.

Aug 1, 2017

$x = 13$

Refer to the explanation for the process.

#### Explanation:

Solve:

$15 - 2 \sqrt{x + 3} = 7$

Subtract $15$ from both sides.

$- 2 \sqrt{x + 3} = 7 - 15$

Simplify.

$- 2 \sqrt{x + 3} = - 8$

Square both sides.

${\left(- 2 \sqrt{x + 3}\right)}^{2} = {\left(- 8\right)}^{2}$

Simplify.

$4 \left(x + 3\right) = 64$

Divide both sides by $4$.

$x + 3 = \frac{64}{4}$

Simplify.

$x + 3 = 16$

Subtract $3$ from both sides.

$x = 16 - 3$

Simplify.

$x = 13$